Going back to my basic training drinking water was drummed into us as being THE major priority in survival situations. It is possible to survive without food for longer than you would expect but, water is needed to keep the bodys vital organs and functions ticking over.Renal failure kicks in first causing your blood eloctrolyte levels to go pear shaped leading to loss of concentration and confusion which affects your ability to do and think straight. Dehydration kills before malnutrition even gets a look in. That said, the environment on Gardner island doesn't lend itself easily to getting said potable water. You would need to search out the part of the island that has the highest humidity levels i.e. away from sea breezes, to stand any chance of gaining water from airborne water droplets. Coconuts? If you can find them on the ground and, get them open but, don't rely on them for too long they don't do your digestive system any good after prolonged consumption. Rain! If it does, collect more than you will ever need but, you'll need something to collect it in and, protect it thereafter from evaporation, a cup or two won't last 10 minutes. You would need a couple of jerry cans full to tide you over to the next rain fall or, to cover your efforts in water collection from airborne water droplet collection, coconut harvesting etc...
Of course don't forget once dehydration has set in all this becomes impossible
IMHO and experience
Jeff